Chapter 6.1, Problem 108E

Landscaping Formula A shrub is planted in a 100-ft-wide space between buildings measuring 75 ft and 150 ft tall. The location of the shrub determines how much sun it receives each day. Show that if θ is the angle in the figure and x is the distance of the shrub from the taller building, then the value of θ (in radians) is given by

$\theta =\pi -\arctan \left(\frac{75}{100-x}\right)-\arctan \left(\frac{150}{x}\right).$